Question

PQRS is a cyclic quadrilateral. If $\angle Q=\angle R={65}^{\circ },$ then find $\angle P$= ___ and $\angle S$ = __.

• A. ${115}^{\circ },{115}^{\circ }$
• B. ${115}^{\circ },{125}^{\circ }$
• C. ${120}^{\circ },{110}^{\circ }$
• D. ${125}^{\circ },{115}^{\circ }$

Answer 1

The correct option is A ${115}^{\circ },{115}^{\circ }$

Consider the cyclic quadrilateral PQRS. Since opposite angles are supplementary,
$\angle P+\angle R={180}^{\circ }.$
$\therefore \angle P={180}^{\circ }–\angle R={180}^{\circ }–{65}^{\circ }={115}^{\circ }$
Similarly,
$\angle Q+\angle S={180}^{\circ }.$
$\therefore \angle S={180}^{\circ }–\angle Q={180}^{\circ }–{65}^{\circ }={115}^{\circ }.$